Capobianco, Silvio and Kari, Jarkko and Taati, Siamak - Post-surjectivity and balancedness of cellular automata over groups

dmtcs:3918 - Discrete Mathematics & Theoretical Computer Science, September 15, 2017, Vol 19 no. 3
Post-surjectivity and balancedness of cellular automata over groups

Authors: Capobianco, Silvio and Kari, Jarkko and Taati, Siamak

We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injective, post-surjective cellular automata are reversible. Moreover, on sofic groups, post-surjectivity alone implies reversibility. We also prove that reversible cellular automata over arbitrary groups are balanced, that is, they preserve the uniform measure on the configuration space.


Source : oai:arXiv.org:1507.02472
Volume: Vol 19 no. 3
Section: Automata, Logic and Semantics
Published on: September 15, 2017
Submitted on: July 18, 2017
Keywords: Mathematics - Dynamical Systems,Nonlinear Sciences - Cellular Automata and Lattice Gases,37B15, 68Q80, 37B10


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